Increasing Crack Length Research Articles

BTAP dynamic model establishment and influence analysis of marine two-stage herringbone gear transmission system considering cracks

To reveal the influence of cracks on the vibration characteristics of marine two-stage herringbone gear transmission system (TSHBGTS), a 48 degree of freedom bending-torsional-axial-pendular (BTAP) dynamic model of the system was established, which took into account the influence factors such as error, time-varying meshing stiffness (TVMS), torsional stiffness, support stiffness, tooth surface friction, and undercut. In the model, the TVMS of each gear pair in the Two-stage herringbone gear system with cracks was calculated by using the potential energy method, and the TVMS variation rule under different lengths, depths, and angle parameters of cracks was analyzed. The Runge-Kutta numerical integration method was used to solve the problem. The influence of different crack degrees on the vibration of each position of the TSHBGTS was analyzed. The influence of different crack degrees on the vibration response of was tested through tests. The difference in mechanical vibration between the normal gear and cracked gear was analyzed by using the frequency domain diagram and time domain diagram, and the influence mechanism of cracks on vibration characteristics was revealed. The results show that when the gear cracks, the TVMS of the gear decreases, and with the increase of the crack depth and length, the TVMS of the gear pair will gradually decrease. With the increase of crack depth and length, the TVMS of the gear pair is greatly reduced, and there is a periodic impact phenomenon in the time domain response of the system. With the continuous expansion of the crack, the impact phenomenon becomes more and more serious. In the frequency domain response, a modulated sideband centered on the meshing frequency appears. When the crack is generated and the crack degree increases, a small noise frequency is generated near the frequency doubling and increases with the growth of the crack. The correctness of the theoretical analysis model is verified through experiments, and the research results can provide a theoretical basis for the fault diagnosis of the herringbone gear transmission systems with cracks.

Atomistic analyses of fracture in [formula omitted], [formula omitted] and lamellar [formula omitted] - [formula omitted] Ti single crystals

In this work, molecular dynamics simulations are employed to investigate crack growth behavior and related microstructural evolution in α-Ti, β-Ti, and lamellar-Ti single crystals under plane strain conditions. It is observed that the crack growth is independent of the initial crack length in α-Ti while it depends on the initial crack length in β-Ti and lamellar-Ti. The crack growth in β-Ti increases monotonically with an increase in initial crack length. However the crack growth in lamellar-Ti does not increase monotonically with respect to the initial crack length since the crack tip of different initial cracks may lie in α-phase, β-phase, or α−β interface in lamellar-Ti. Significant structural changes (α to β phase transformation) due to the applied deformation are not observed in α-Ti. For both β-Ti and lamellar-Ti, the β-phase is transformed into different variants of the α-phase. Dislocation density is the largest for lamellar-Ti followed by β-Ti and α-Ti. The critical strain energy release rate is the largest for β-Ti and it is lowest for α-Ti. The Gc for α-Ti decreases with an increase in initial crack length and does not appear to be much sensitive to the initial crack length. In the case of β-Ti and lamellar-Ti, Gc shows a strong dependence on the initial crack length and the variation of Gc relative to the initial crack length can be well described by an exponentially decaying function.

Effect of gap and overlap on mode II interlaminar fracture toughness of automated fiber placement prepreg laminates

Automated Fiber Placement (AFP) technology facilitates the manufacturing process of composite structures with complex geometry owing to its high efficiency and accuracy. However, the unavoidable imperfections induced by the automated layup method bring challenges to the stability of the final mechanical properties of composites. The influence of AFP-induced gaps and overlaps on the mode II interlaminar fracture process of oven-cured laminates is experimentally investigated and explicitly revealed. End-Notched Flexure (ENF) tests were performed to measure the interlaminar fracture toughness of unidirectional laminates under three different defect configurations, namely “Gap” “Overlap” and “Gap & Overlap”. A marginal decline (about –1.2% in non-precracked tests, –5.1% in precracked tests) and an obvious increase (about 15.2% in non-precracked tests, 5.2% in precracked tests) in fracture toughness were observed for the “Gap” group and the “Overlap” group, respectively. Fractographic studies which involve the metallographic observation and Scanning Electron Microscopy (SEM) observation revealed that the increases in fracture area and crack length helped improve the fracture toughness of the “Overlap” group. However, the resin-rich area with high porosity induced by gaps was detrimental to the delamination resistance. To capture the interlaminar stress distribution local to imperfections, a three-dimensional numerical model was established. Gap defects facilitate the local delamination process, and the overlap defect postpones the damage onset and the propagation.

Research on crack detection method of anvil based on eddy current sensor

In the process of synthetic diamond, as a key component of high-temperature and high-pressure devices, the crack of the six-sided press anvil is easy to cause serious safety accidents. This paper introduces a crack detection method based on an eddy current sensor. Through the detection system, the induced voltage value in the receiving coil is obtained when the hammer has cracks, so as to judge whether there are cracks in the hammer. The results show that when there is a crack in the anvil, the induced voltage in the receiving coil will increase significantly. When the crack length, width, and depth increase, the induced voltage in the receiving coil will increase significantly. It is proved that eddy current testing is feasible in anvil detection.

An analytical approach for the fracture characterization of concrete under cyclic loading

Many civil engineering infrastructures frequently encounter repetitive loading during their service life. Due to the inherent complexity observed in concrete, like quasi-brittle materials, understanding the fatigue behavior in concrete still poses a challenge. Moreover, the fracture process zone characteristics ahead of the crack tip have been observed to be different in fatigue loading than in the monotonic cases. Therefore, it is crucial to comprehend the energy dissipation associated with the fracture process zone (FPZ) due to repetitive loading. It is well known that energy dissipation due to cyclic loading provides a better understanding of the fracture behavior of concrete. Under repetitive load cycles, concrete members exhibit a two-stage energy dissipation process. Experimentally, it has been observed that the rate of energy dissipation decreases initially with an increase in crack length and subsequently increases. In this work, an attempt has been made to propose an analytical expression to predict energy dissipation as a function of crack length, and the fully developed fracture process zone length under cyclic loading condition.

Advantages of the extended finite element method for the analysis of crack propagation in power modules

• XFEM and Level set methods with submodelling has been implemented in this study. • Method easily allows inclusion of crack growth in IGBT wire bond reliability analysis • Bond wire diameter and loop height significantly affect IGBT wire bond reliability. • Wire bond degradation parameter values decrease with increasing crack length. • For similar load density, smaller wire diameter produces longer wire bond lifetime. The techniques of extended finite element method, level set method and the submodelling approach are implemented in this study to model crack and crack growth in ultrasonically bonded thick aluminium wire for the IGBT power electronics modules under different loading conditions for the purpose of lifetime prediction and reliability assessment during design and manufacturing stages. The crack growth and lifetime prediction were performed under cyclic fatigue passive thermal cycling and active power cycling for the bond wire lift-off failure mechanism while the J-integral for different heel crack lengths are predicted under mechanical loads. The analyses showed that the techniques implemented in this paper are effective for modelling such complex geometries and loading conditions and can easily be integrated in a virtual design platform for power electronics. The accuracy of the technique is evaluated by comparing with trends in the published experimental tests and simulation results as well as the standard finite element method which are all in a good agreement. The wire bond crack growth rate under cyclic loading is strongly influenced by the bond thickness and loading conditions.

Effects of Static Pressure on Failure Modes and Degree of Fracturing of Sandstone Subjected to Inter-Hole Pulsed High-Voltage Discharge

This research aims to explore the fracturing behaviors of sandstone subjected to pulsed high-voltage discharge (PHVD) under different static pressures. An experimental method of rock fracturing induced by inter-hole PHVD was proposed. The static pressure was applied to the specimens, then the proposed method was applied to induce electrical breakdown testing under static loading. The microscopic fracture morphology of the sandstone was observed. The influences of the direction and level of static pressure on the crack length and fractal dimension of sandstone under the effect of PHVD were discussed. The results indicated that in the absence of static pressure, there are a discharge channel and multiple radial cracks in the sandstone after electric breakdown. The microscopic analysis implies that rock failure in the zone around the discharge channel is mainly influenced by the high temperature; while radial cracks are induced by shock waves. When static pressure is vertical to the discharge channel, tensile and compressive stresses concentrate in different parts around the discharge channel, which can remarkably alter the distribution zone and propagation path of cracks. In addition, the fractal dimension and total length of cracks first decrease, then increase with increasing static pressure. When static pressure is parallel to the discharge channel, the distribution characteristics and propagation direction of cracks are unchanged; however, under this loading mode, circularly distributed hoop tensile strains are generated at the zone around the discharge channel, which enables the fractal dimension and crack length increase with increasing static pressure.

Research on Buckling Load of Cylindrical Shell with an Inclined through Crack under External Pressure and Its Solution

In order to evaluate the reliability of cracked cylindrical shell effectively and reasonably, study the load capacity of cracked structures and understand the failure modes of cracked structures, in this paper the finite element method is adopted for cylindrical shells with mixed mode crack. The finite element models of cylindrical shell with an inclined through crack under external pressure were established by finite element method, the elastic and elastic-plastic buckling loads were calculated. The influences of crack length (c), crack angle (θ), cylindrical shell length-radius ratio (L/R), radius-thickness ratio (R/T), boundary conditions on buckling load were explored. The analysis of cracked cylindrical shells with simple support on buckling load shows that the load bearing capacity of cracked cylindrical shells decreases with the increase of length- radius ratio, radius-thickness ratio and crack inclination angle. The increase of crack length can weaken the bearing capacity of cylindrical shell. The variation of elastic-plastic buckling load is consistent with that of elastic buckling load. Under the clamped support, the variation of buckling load is consistent with the buckling load of cracked cylindrical shell with simple support, and the buckling load of cracked cylindrical shell with clamped support is evidently higher than that of simple support. The post-buckling analysis further shows that the changes of crack inclination angle and crack length do not affect the variation modes of pre-buckling and post-buckling deformation of cracked cylindrical shells, but affect the load capacity. The relationship between buckling load of different boundary conditions (simply supported and clamp-supported) and geometrical parameters (length-radius ratio, radius-thickness ratio, crack length and crack Angle) was obtained by nonlinear regression. The results of solution can predict the buckling load of cylindrical shell with an inclined through crack.

Experimental investigation on the correlation between critical storage of elastic strain energy and crack extension in elastic–plastic materials

AbstractTo better solve the issues of steady crack extension with broad plasticity and the crack‐related problems in general yielding situations when the assumption of small‐scale plastic yielding fails, it is of great significance to further study the macroscopic mechanism of crack extension. In this paper, a new insight into the elastic–plastic crack extension is proposed on the foundation of critical storage of elastic strain energy (SESE). The feasibility of the new methodology is validated by designing and implementing two different experimental schemes in three typical elastic–plastic materials. The experimental results indicate that the critical SESE decreases linearly with the increase of crack length and U‐notch initial length. Besides, the SESE release rate is obtained through experimental and theoretical methods, and they are in the same order of magnitude and their value sequences are also accordant with all tested materials. Therefore, this investigation provides a new approach to characterizing crack extension in elastic–plastic materials.

Numerical evaluation of fracture behavior of split concrete beams reinforced with steel sheet

Since the parameters affecting the strengthening of cracked beams and their failure behavior after strengthening are very important, this research is devoted to the numerical investigation of the failure behavior of cracked concrete beams reinforced with steel sheet. The investigated beams have an initial crack in the middle of the span and are reinforced with a steel layer under the beam. Using the finite element method and non-linear static analysis, the bearing capacity of the samples, the growth and opening of the crack opening have been evaluated. First, in order to evaluate the accuracy of the modeling, the results obtained with the data obtained from the existing laboratory work were compared, and after ensuring the correctness of the modeling, the effect of changing various parameters, including sheet thickness, mechanical characteristics of concrete, initial crack length, was investigated. The results show that the load-opening diagrams of the crack openings have two maximum load points, the first and second maximum points increase with the increase of concrete strength and sheet thickness, and due to the increase in the initial crack length, the first maximum point decreases, while the maximum point The second remains almost unchanged.

Comparison of sensitivity in nonlinear ultrasonic detection based on Lamb wave phase velocity matching mode

ABSTRACT In nonlinear ultrasonic damage detection, the appropriate Lamb wave mode to accurately characterise the nonlinearity attributed to the material damage should be selected important. However, an effective mode is more difficult to select practically as impacted by the dispersion and multi-mode characteristic of the Lamb wave. In this study, based on the dispersion curve of Lamb waves, the modes meeting the second harmonics and third harmonics phase velocity matching were given, and the nonlinear cumulative effects exerted by different modes on fatigue cracks were compared. In addition, an investigation was conducted on the amplitude change of the second and third harmonics signal of the identical fatigue damage. The results show that the harmonic amplitude decreases with the increase of the fatigue crack length. The third harmonics under the two modes are more sensitive to fatigue damage than the second harmonics. Moreover, the amplitude of the third harmonic excited by S1 mode exceeds that of the other mode. As the fatigue crack length increases, the relative second- and third-order nonlinear coefficients generated by S1 mode have approximately the same trend, first increasing and then decreasing. The results reveal that the third harmonic under S1 mode could more effectively characterise fatigue damage.

Experimental study on the energy evolution law during crack propagation of cracked rock mass under impact loads

Rock dynamic fracture is usually accompanied by numerous energy loss, to reveal energy evolution laws during rock dynamic fracture, the single cleavage triangle (SCT) specimens made by two types of sandstone are implemented to conduct dynamic fracture tests by using the split Hopkinson pressure bar (SHPB) device. The dynamic stress distribution law and the energy evolution law can be obtained according to the strain history of cracked rock mass subjected to impact loads. Crack propagation gauges (CPG) were applied to measure crack propagation speed, dynamic stress intensity factor (DSIF) and dynamic energy release rate can be determined by using an experimental–numerical method with the help of the software COSMOL. The experimental results show a physical pseudo-healing of the crack due to the short closure of the crack after its arrest under impact loads. The crack propagation speed and the DSIF show a certain oscillatory with the increase of crack length, the DSIFs at crack initiation are 0.2 ∼ 0.8 of the maximum value. The history of dissipated energy has a slow decrease after they reach a peak during 300 μs ∼ 350 μs, whose curves after the peak contain two stages: stage I is that the absorbed energy of the SCT specimen is mainly transformed into the transmitted energy; stage II is that it will be reflected energy. The input energy overtakes the consumed energy by new crack formation to drive the crack propagation and the test results of sandstone specimens show that 2.11 ‰ to 4.44 ‰ dissipated energy is implemented to drive crack propagation. The energy and stress are released more significantly around the crack tip before the crack arrest.

Atomistic scale behaviors of intergranular crack propagation along twist grain boundary in iron under dynamic loading

Due to alternative exchange between single and double-teeth meshings, the upper part of gear tooth is subjected to dynamic tensile stress whose growth rate presents rectangular fluctuation. This work investigates the atomistic scale behaviors of intergranular crack propagation along twist grain boundary in body-centered cubic (bcc) iron under dynamic tensile stress. The effects of driving force and contact ratio are fully discussed. Results show that only stacking faults with face-centered cubic (fcc) atoms can be formed in lower monocrystal portion. Edge dislocations in upper monocrystal portion are suppressed by intergranular crack cleavage. Critical stresses for stacking fault nucleation and intergranular crack cleavage vary with driving force and contact ratio. By calculating actual stress intensity factor at crack tip, variations of critical stresses are found to be attributed to the variations of time-dependent factors. Although critical stresses vary with driving force and contact ratio, the effects of these factors on the growths of crack length and plastic zone are not obvious in the early stage of intergranular crack propagation. Accumulated plastic strain energy before intergranular crack cleavage is independent of driving force and contact ratio. Departing from the early stage, the growth rates of crack length and plastic zone increase significantly with an increase in driving force or a decrease in contact ratio. However, the final ductile level of intergranular crack propagation cannot vary with contact ratio and large driving force. By applying dynamic load, this work can be used to reveal the atomistic scale mechanism of gear failure. The results can provide a good reference for gear safety design.

Vertical crack distribution effect on the TBC delamination induced by crack growth from the ceramic surface and near the interface

The propagation of vertical crack on the surface of thermal barrier coatings (TBCs) may affect the interface cracking and local spallation. This research aims to establish a TBC model incorporating multiple cracks to comprehensively understand the effects of vertical crack distribution on the coating failure. The continuous TGO growth and ceramic sintering are together introduced in this model. The influence of the vertical crack spacing and non-uniform distribution on the stress state, crack driving force, and dynamic propagation is examined. Moreover, the influence of coating thickness on the crack growth driving is also explored. The results show that large spacing will lead to early crack propagation. The uniform distribution of vertical cracks can delay the spallation. When the spacing is less than 4 times ceramic coat thickness, the cracking driving force will come in a steady-state stage with the increase of vertical crack length. Prefabrication of vertical cracks with spacing less than 0.72 mm on the coating surface can greatly decrease the strain energy. The results in this study will contribute to the construction of an advanced TBC system with long lifetime.

Linear Elastic Fracture Mechanics Assessment of a Gas Turbine Vane.

This work assesses the crack propagation at the most critical point of a second stage of a gas turbine blade by means of linear elastic fracture mechanics (LEFM). The most critical zone where the crack may nucleate, due to a combination of thermo-mechanical loads, is detected with an uncracked finite element (FE) model pre-analysis. Then the sub-modelling technique is used to obtain more precise results in terms of stresses within the area of interest. Simulations of the state of stress at the crack apex are performed through an FE model, using the Fracture Tool within ANSYS Workbench, and the stress intensity factors (SIFs) are determined accordingly. The Fracture Tool was previously verified on a simple model, and the results were compared with its analytical solution. Finally, the evaluation of the crack growth due to fatigue stress, creep, and oxidation is performed through in-house software called Propagangui. The crack behavior is estimated along with the component life. Results show an unexpected decrease in KI with increasing crack length and slowing of the crack growth rate with crack propagation. A detailed analysis of this behavior emphasizes that the redistribution of the stresses at the crack apex means that unstable propagation is not expected.

Experimental study on fracture properties of dam concrete under post‐peak cyclic loading based on DIC and acoustic emission techniques

AbstractIn order to study the fracture properties of dam concrete under post‐peak cyclic loading, wedge splitting tests with three loading rates were performed on notched cubic specimens. Meanwhile, the acoustic emission (AE) and digital image correlation (DIC) technologies were used to monitor crack propagation in the specimens. As the loading rate increases, the peak load increases, and stiffness degradation increases. The cumulative AE counts show a step increasing trend and exhibit a Kaiser effect, which decreases via the post‐peak cyclic loading procedure and increases as the loading rate increases. The AE energy fluctuates markedly, and b value fluctuates frequently with an increasing loading rate. As the loading rate increases, the strain recovery rate decreases, and the permanent crack increases. The effective crack length gradually and steadily increases, and as the loading rate increases, the growth rate of the effective crack length increases.

Exploiting fractal features to determine fatigue crack growth rates of metallic materials

An alternative approach to the classical fracture mechanics equation to quantify the fatigue crack growth rate is proposed and examined. The method exploits the fractal features of the propagating fatigue crack. The reference crack growth response of AISI 410 martensitic stainless steel is established using compact tension C(T) specimens. Fractal analysis of microscopic images along the edge length of the crack establishes the fractal dimensions, dF of the fatigue crack. The box-counting algorithm is developed for the fractal analysis based on optical images of the crack at 100X magnification and the resolution of 1090 pixels/mm. Results show that the crack initially exhibits a Euclidean nature (dF ≈ 1). The fractal dimension increases steadily with increasing crack length in the Paris crack growth rate region with 1.05 < dF < 1.24. The corresponding stress intensity factor range varies between 18 ≤ ΔKI ≤ 40 MPa√m. The fractal dimension, dF correlates linearly with the normalized stress intensity factor range, ΔKKIC within the Paris crack growth region. This enables the multifractal fatigue crack growth rate equation to be established in terms of the fractal dimension, Paris coefficient and exponent, and fatigue fracture properties of the material. The fatigue crack growth rate of the material could then be determined using the multifractal fatigue crack growth rate model without requiring the geometry factor of the crack.

Theoretical Analysis of Stress Intensity Factor for Two Asymmetric Cracks Emanating from Water Conveyance Tunnel

The water conveyance tunnel has been widely applied in tunnel engineering, which may be subjected to compressive stress and shear stress from rock and faults, respectively. The internal pressure caused by water in the tunnel will make the appearance of cracks and propagation, resulting in disasters. In order to study the effects of the cracks and compressive stress on the cracked tunnel model, a plane model containing a circular hole with two unequal cracks under the compression loads, shear stress and internal pressure was established in this study. Complex variable function and conformal mapping function were implemented to theoretically derive the stress intensity factors (SIFs) at the crack tip in the rock mass, the numerical simulation was conducted to validate the theoretical solutions. The results indicate that the numerical results using the ABAQUS code were in good agreement with the theoretical solutions. The effects of compressive stress, shear stress, internal pressure, crack length and crack inclination angle on model II SIFs were discussed, the initiation angle and initiation pressure of different rock materials were also studied. When the crack inclination angle changes from [Formula: see text] to [Formula: see text], the tunnel is easily destroyed. With the increase of the right crack length, the increasing rate of the SIFs increases quickly first and then linearly, however, the left crack length has a slight effect on SIFs. When the crack inclination angle is [Formula: see text], the crack initiation angle reaches the maximum value.

Numerical Investigation of the Influence of Ultimate-Strength Heterogeneity on Crack Propagation and Fracture Toughness in Welded Joints.

The mechanical properties of dissimilar metal-welded joint materials are heterogeneous, which is an obstacle to the safety evaluation of key welded structures. The variation of stress–strain conditions at the crack tip caused by mismatch of material mechanical properties in dissimilar metal-welded joints is an important factor affecting crack propagation behavior. To understand the influence of uneven distribution of ultimate strength of the base metal and the welded metal on the crack propagation path, fracture toughness, as well as the mechanical field at the crack tip in the small-scale yield range, the user-defined field variable subroutine method is used to express continuous variation characteristics of welded joint ultimate strength in finite element software. In addition, the J-integral during crack propagation is calculated, and the effect of the ultimate strength on the J-integral and the stress field at the crack tip are analyzed. The results show that as the crack propagation direction is perpendicular to the direction of ultimate strength, the gradient of ultimate strength increases from |Gy|= 50 to |Gy|= 100 MPa/mm, the crack deflection angle increases by 0.018%, and the crack length increases by 1.46%. The fracture toughness of the material decreased slightly during crack propagation. Under the condition that the crack propagation direction is the same as the direction of ultimate strength, the crack propagation path is a straight line. As the gradient of ultimate strength increases from Gx = 50 to Gx = 100 MPa/mm, the crack propagation length decreases by 5.17%, and the slope of fracture toughness curve increases by 51.63%. On the contrary, as the crack propagates to the low ultimate strength side, the crack propagation resistance decreases, the ultimate strength gradient increases from Gx = −100 to Gx = −50 MPa/mm, and the slope of the fracture toughness curve decreases by 51.01%. It is suggested to consider the relationship between crack growth behavior and ultimate strength when designing and evaluating the structural integrity of cracks at the material interface of dissimilar metal-welded joints.

Numerical Analysis of Fracture Failure Behavior of Refractory Lining in Coal-Water Slurry Gasifier.

Fatigue crack fracture is one of the main reasons for the failure of a refractory lining in a coal-water slurry gasifier. To explore the fracture failure behavior of a refractory lining during the operation of a gasifier, the stress intensity factor (SIF) and J-integral at crack front were calculated by the finite element method, and a crack growth model for the refractory was established. At the same time, the effects of different crack length, depth, and angle on the stress and SIF, as well as J-integral distribution around the crack-tip, were presented. The simulation results demonstrated that very large stresses occurring at the crack tip and the distribution regulation of KI and J-integral along the crack front for surface cracks were similar. The maximum values occurred near the two ends of the crack (θ = 0°, 180°), and the minimum values appeared near the deepest crack front (θ = 90°). KI and J-integral values at the same position increase with increasing crack length and depth and decrease with the angle of crack when the a/c was kept constant. Furthermore, J-integral results indicated that excessive crack depths were likely to cause destabilizing crack growth. These results have provided a reliable theoretical basis for fracture analysis and life prediction of the refractory lining in a gasifier.